Problem: Simplify the following expression: $t = \dfrac{x^2 - 11x + 18}{x - 2} $
First factor the polynomial in the numerator. $ x^2 - 11x + 18 = (x - 2)(x - 9) $ So we can rewrite the expression as: $t = \dfrac{(x - 2)(x - 9)}{x - 2} $ We can divide the numerator and denominator by $(x - 2)$ on condition that $x \neq 2$ Therefore $t = x - 9; x \neq 2$